Abstarct: Due to the flexibility of the compliant mechanisms (CMs), they are utilized to perform mechanical operations (such as motion transfer and power transfer). From the viewpoint of performance, CMs have some advantages over traditional ones, such as higher precision, integrated design, and lower manufacturing costs. However, CMs also have limitations such as limited range of motion. Topology optimization of CMs considering curved beam elements is the main aim of the current study. The straight beams and flexure hinges are usually used to design CMs, but curved beams can improve their performance. The existence and non-existence of the beam elements in the initial synthesis, as well as their type (straight or curved beams), are the most important design variables of this optimization problem. The objective function of this problem is to increase the mechanical and geometrical advantages (MA and GeA) of the CMs. In the current study, two methods including genetic and imperialist competition algorithms (GA and ICA) were used to derive the optimal structure of the CMs. In addition, the results of these two algorithms are also compared for different examples. The optimized CMs that consist of beam elements are analyzed with the finite element method. The results show that the existence of curved beams in CMs may improve their performance and increase the defined objective functions. In addition, the comparison of the two algorithms used shows that ICA performs better than the GA, which is one of the most powerful methods in optimization.